More complex approaches to aggregation (e.g.Under impartial views, conditional on a given god (or gods), you won't change the aggregate: it's already undefined, +infinity or -infinity, and adding one more person to Heaven or Hell won't make a difference to that value.Under decision-theoretic uncertainty assigning some credence to unbounded EU maximization with infinities, low probabilities of Heaven or Hell might still not dominate. There are plausible alternative decision theories that don't require (but may permit) choosing extremely low probability bets of extremely high payoffs, like EU maximization with bounded utility functions and stochastic dominance.Some other decision theory might be preferable, or we can allow decision-theoretic uncertainty. If the bases for allowing and treating infinities this way require the violation of some plausible requirements of rationality or require ad hoc and suspicious beliefs about what kinds of values are possible (infinity is possible but finite values must be bounded), then it's at least not obvious that we're normatively required to treat infinities this way. Unbounded finite values can lead to violations of the sure-thing principle, as well as vulnerability to Dutch books and money pumps (e.g. Furthermore, if we're allowing infinities, especially as limits of aggregates of finite values like an eternity of positive welfare, then it would be suspicious to not allow unbounded finite values at least in principle. However, infinite and unbounded values violate the continuity axiom. This could reduce to EU maximization with some prior steps where we ignore equiprobable parts of distributions with the same values. This could be justified through the application of plausible rationality axioms directly, in particular the independence axiom. In response to 1, you might say that we should maximize the probability of +infinity and minimize the probability of -infinity before considering finite values.(I got this from a paper, but I forget which one maybe something by Alan Hájek.) There's always a nonzero chance you will end up choosing the right religion and be rewarded infinitely and a nonzero chance you will end up choosing badly and be punished infinitely, so the EU is +infinity + (-infinity) = undefined. All options maximize expected utility (EU), since the expected utility will be undefined (or infinite) regardless.I would obviously love to hear any other arguments.
#Pascals wager how to
I also don't know how to go about rejecting infinite utilities if it turns out I have to. I've also heard the argument that we should reject all infinite utilities – for now it seems to me that Pascal's Wager is the only example where the probabilities don't cancel out, so I don't have any paradoxes or inconsistencies, but this is probably quite a fragile position that could be changed. It seems quite clear that the probability of a god that matches the god of existing religions is far more likely than a god that is the opposite, therefore they don't cancel out because the expected utilities aren't equal. I have heard the argument that there could be a god that reverses the positions of heaven and hell and therefore the probabilities cancel out, but this doesn't convince me. I'm honestly surprised there isn't much discussion about it in this community considering it theoretically presents the most effective way to be altruistic. I am a utilitarian and I struggle to see why I shouldn't accept Pascal's Wager. Edit: To clarify, when I say "accept Pascal's Wager" I mean accepting the idea that way to do the most (expected) good is to prevent as many people as possible from going to hell, and cause as many as possible to go to heaven, regardless of how likely it is that heaven/hell exists (as long as it's non-zero).
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